26
CMOS Circuit Design, Layout, and Simulation
*** Figure 1.32 ***
Vout
AC 1
1k
10 nH
*#destroy all
*#run
*#plot db(vout)
10 pF
.AC lin 100 400MEG 600MEG
Iin Vout 0 DC 0 AC 1
R1 Vout 0 1k
L1 Vout 0 10n
C1 Vout 0 10p
.end
Figure 1.32 Determining the Q, or quality factor, of an LC tank.
Frequency Response of an Ideal Integrator
The frequency response of the integrator seen in Fig. 1.33 can be determined knowing the
op-amp keeps the inverting input terminal at the same potential as the non-inverting input
(here ground). The current through the resistor must equal the current through the
capacitor so
V in
V
out
R 1/jZC
(1.13)
0
or
V out
V in
1
jZRC
1j˜0
0 jZRC
(1.14)
The magnitude of the integrator's transfer function is
V out
V in
1 2 0 2
0 2SfRC
2
2
1
2SRCf
(1.15)
while the phase shift through the integrator is
V
‘ out
V in
§
·
¨ 1 0
¸
2SRCf
¨ tan
tan 1
¸
1
0
¨
¸
© 0
¹
S/2
90
(1.16)
Note that the gain of the integrator approaches infinity as the frequency decreases towards
DC while the phase shift is constant.
Unity-Gain Frequency
It's of interest to determine the frequency where the magnitude of the transfer function is
unity (called the unity-gain frequency, fun.) Using Eq. (1.15), we can write